In certain high density circuit board applications such as board to board interconnections one of the mating connectors is attached to the edge of one of the boards and the other connector is either attached to the edge or on the surface of the other board. Such connectors, when mounted to the edge of the board, occupy less board space than their surface mount counterparts, and therefore are more desirable in these applications. Examples of these types of connectors are disclosed in U.S. Pat. Nos. 5,199,885 and 5,127,839 which issued to Korsunsky et al. on Apr. 6, 1993 and Jul. 7, 1992 respectively. As the circuitry on these circuit boards becomes more dense the edge mounted connector must become correspondingly smaller resulting in very delicate contacts. Any variation in alignment during assembly of the connector to the circuit board may cause the contacts to become damaged. Therefore, precise alignment is necessary. However, variations in the thickness of the circuit board due to allowable manufacturing dimensional tolerances make it difficult to consistently and accurately align a high density edge mounted connector with the edge of the board. This is especially the case where the connector includes contacts that must be connected to circuitry on both sides of the board. What is needed is an assembly machine having the ability to sense the actual thickness of the circuit board and align the connector so that the centerline between the opposing contacts is substantially coincident with the actual center plane of the circuit board during assembly. This will effectively split the difference in board thickness variation between the two rows of opposing contacts, thereby reducing the chance of damaging the contacts. The present invention is directed to this capability.